find a parametric representation of the solution set of the linear equation. (enter your answer as a comma-separated list of equations. use t as your parameter.)
To represent the solution set of a linear equation parametrically, we introduce other parameters like s and t for the free variables.
Every linear equation has n - 1 free variables where n is the number of variables.
For x + y + z = 2, we have 3 variables and 3 - 1 = 2 free variables.
First, let y and z be the free variables, we first solve the linear equation for x to get:
x = 2 - y - z
Therefore , the parametric representation of the solution set is given by :
x = 2 - s -t
y = s
z = t
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Cory's baseball bat weighs 25.64 ounces, and his glove weighs 13.05 ounces. How much does his baseball gear weigh altogether?
Answer: 38.69
Step-by-step explanation:
Just do 25.64 + 13.05
Answer: 38.69
Step-by-step explanation:
Simplify 6a^2b^-2/8a^-3b^3
Assume a≠0 b≠0
Answer:
3/4
Step-by-step explanation:
reducing 6/8 would be 3/4, and if a and b = 0, then anything multiplied by 0 would be nothing so there wouldn't be and variables
Answer:
the answer is C
Step-by-step explanation:
edge
find the distance between the points (-5,7) and ( -5,-4)
Answer:
11
Step-by-step explanation:
Matching: Connect the correct statement with the corresponding picture. There are multiple correct statements per picture.
A) System is consistent and independent
B) System is consistent and dependent
C) System is inconsistent
D) Only one solution to system
E) Infinitely many solutions to system
F) No solutions to system
Answer:
Figure 1: A , D
Figure 2: B, E
Figure 3: C, F
Hope that helps!
The equation of the line in the graph is y = x + .
Answer:
Step-by-step explanation:
y=x+b
find the volume v of the described solid s. the base of a solid s is the region enclosed by the parabola y = 4 − x2 and the x-axis. cross-sections per
The volume v of the described solid s = 8 cubic units .
Given : a parabola y = 4 - ( x ^ 2 )
Writing eq . y = 4 - ( x ^ 2 ) in terms of x ,
( x ^ 2 ) = 4 - y
x = ± [tex]\sqrt{4 - y}[/tex]
A ( y ) = ± [tex]\sqrt{4 - y}[/tex] * ( ± [tex]\sqrt{4 - y}[/tex] )
A ( y ) = 4 - y
Volume the given solid = [tex]\int\limits^4_0 {( 4 - y )} \, dy[/tex]
= 4 ( 4 ) - [ ( 4 ^ 2 ) / 2 ]
= 16 - 8
= 8
Hence , the volume v of the described solid s = 8 cubic units .
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What is 22 lb day in oz h?
Answer:
352 OZ
Step-by-step explanation:
One pound = 16 OZ
take 22 and multiply it by 16
22 x 16 = 352
Answer:
15 ounces per hour
Step-by-step explanation:
This is dimensional analysis, so we need to find conversion factors for ounces per pound and hours per day. Once we have those we write the equation such that the units we need are left and the others cancel:
22lb/1 day x 16 ounces/1 lb x 1 day/24hrs = 14.66666666666 ounces per hour
Since the problem was written with no decimals, our answer probably shouldn't either and in most cases like this we want to round to the nearest whole number, which is 15.
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Choose the point-slope form of the equation below that represents the line that passes through the point (−1, 6) and has a slope of −3.
Answer:
y - 6 = - 3(x + 1)
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Here m = - 3 and (a, b) = (- 1, 6) , then
y - 6 = - 3(x - (- 1) ) , that is
y - 6 = - 3(x + 1)
Answer:
your answer would be y - 6 = - 3(x + 1)
Step-by-step explanation:
hopes this helps!:)
i need help how to solve bc this is for a grade
Answer: i think its D
Step-by-step explanation:
Please help 11 points worth
Answer:
positive
cuz i just know :)
good luck
Someone help me out with this question
The answer is A or the 1 selectible option
You just need to look at it from left to right
Simplify the expression
a. x^2
b. x^3
c. x^1/3
d. x^1/2
Answer:
d
Step-by-step explanation:
When you exponent an exponent with another exponent, you multiply them together
[tex]Answer:\ x^\frac{1}{2}[/tex]
Step-by-step explanation:
[tex](x^\frac{1}{6})^3=\\\\ x^\frac{1*3}{6}=\\\\ x^\frac{3}{2*3} =\\\\x^\frac{1}{2}[/tex]
What is the angle relationship between the House and Bank? And is the relationship Congruent or Supplementary?
Answer:
congruent
Step-by-step explanation:
In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.
so yes, they are congruent because they have the same angle
HELP HELP HELP FAST PLS PLS
Marc sold 500 tickets for the school play. Student tickets cost $2 and adult tickets cost $5. Marc's sales totaled $1,789. a) Write a system of equations that can be used to determine how many of each type of ticket Marc sold b) Solve the system to determine how many adult tickets and how many student tickets Marc sold.
Answer:
a) System of equations will be: [tex]x+y=500\: and\:5x+2y=1789[/tex]
b) Number of adult tickets sold = 263
Number of students tickets sold = 237
Step-by-step explanation:
Let:
Number of adult tickets sold = x
Number of students tickets sold = y
a)
As Marc sold total 500 tickets, the expression will be: [tex]x+y=500[/tex]
Student tickets cost $2 and adult tickets cost $5. Marc's sales totalled $1,789.
The expression will be: [tex]5x+2y=1789[/tex]
So, system of equations will be: [tex]x+y=500\: and\:5x+2y=1789[/tex]
b)
Solve the system to find value of x and y
Let:
[tex]x+y=500--eq(1)\\5x+2y=1789--eq(2)[/tex]
Multiply equation 1 by 2 and subtract
[tex]2x+2y=1000\\5x+2y=1789\\-\:\:\:-\:\:\:\:\:\:\:\:\:-\\------\\-3x=-789\\x=\frac{-789}{-3}\\x=263[/tex]
We get value of x = 263
Now finding value of y by putting value of x in eq(1)
[tex]x+y=500\\263+y=500\\y=500-263\\y=237[/tex]
We get value of y = 237
Number of adult tickets sold = x = 263
Number of students tickets sold = y = 237
Find the slope of the line
Answer:
3/4
Step-by-step explanation:
What is the equation of the line that passes through the point (-6,2)(−6,2) and has a slope of -3/2?
Given:
A line passes through the point (-6,2) and has a slope of [tex]-\dfrac{3}{2}[/tex].
To find:
The equation of line.
Solution:
If a line passes though a point [tex](x_1,y_1)[/tex] and has a slope m, then the equation of line is
[tex]y-y_1=m(x-x_1)[/tex]
The line passes through the point (-6,2) and has a slope of [tex]-\dfrac{3}{2}[/tex]. So, the equation of line is
[tex]y-2=-\dfrac{3}{2}(x-(-6))[/tex]
[tex]y-2=-\dfrac{3}{2}(x+6)[/tex]
[tex]y-2=-\dfrac{3}{2}(x)-\dfrac{3}{2}(6)[/tex]
[tex]y-2=-\dfrac{3}{2}(x)-9[/tex]
Add 2 on both sides.
[tex]y=-\dfrac{3}{2}(x)-9+2[/tex]
[tex]y=-\dfrac{3}{2}x-7[/tex]
Therefore, the equation of line is [tex]y=-\dfrac{3}{2}x-7[/tex].
Colton opened a savings account and deposited $1,000.00 as principal. The account earns 11% interest, compounded annually. What is the balance after 8 years? Round your answer to the nearest cent.
Answer:
$2304.5
Step-by-step explanation:
The balance after 8years=P(1+R/100)^t
=1000(1+11/100)^8
=$2304.5
The empirical rule states that, for data having a bell-shaped distribution, the percentage of data values being within one standard deviation of the mean is approximately.
Answer:
empirical rule: about 68% of the data is within 1 standard deviation of the mean.
Step-by-step explanation:
Write an equation of the line passing through point P(0, -1) that is parallel to the line y = - 2x + 3. y =
Answer:6
-3y= 6 - 2x
Answer:
y=-2x-2
Step-by-step explanation:
Parallel means the same slope from the given slope in the statement.
To find the slope-intercept form equation, you must use the point-slope form which is y-y1=m(x-x1).
The given point (0, -1) includes 0 as the x-intercept and -1 as the y-intercept.
Because parallel is the same slope, the slope we'll insert into our equation is -2.
The point-slope form substituted with the given point and slope looks like the following:
y-(-1)=-2(x-0) which can be simplified to y+2=-2x+0
Solve the simplified equation.
y+2=-2x+0
-2 -2
y=-2x-2
That's the final equation.
Hope this helps.
When using Synthetic Division, you can tell if something is a factor if...
1 it has a remainder of over 100.
2. it has a negative remainder.
3.. it has a remainder of zero.
45 WZ is parallel to XY,
SW = 15, WX = 5, SZ =12, WZ= 9 Find XY
S
I
W
Z
Х
Y
Step-by-step explanation:
wz parallel to XYXYS similar WZSXY/WZ=XS/SWXY/9=20/15XY=12My monthly utility bill was $69.86. There was just a rate adjustment and now my bill
is $64.72. To the nearest tenth of a percent, by what percent did my water bill
change?
Write the equation of a line parallel to x = 3 that contains (−4, 5).
Answer:
y=3x+17
Step-by-step explanation:
equation:
y-y¹=m(x-x¹)
substitute with same slope.
y-5=3(x-(-4))
y-5=3x+12
y=3x+17
Help needed!!! Please
Answer:
5
Step-by-step explanation:
distance formula= radical[(x_2 - x_1)^2 + (y_2 - y_1)^2]
= radical[(1-5)^2 + (6-9)^2]
= radical(16+9)
= radical(25)
= 5
.
Solve for x
5x – 7 = 19
Give your answer as an

5x - 7 = 19
Add 7 to both sides:
5x = 26
Divide both sides by 5:
x = 26/5
[tex]5x - 7 = 19[/tex]
Move -7 to another side and become + 7. Whenever we move to another side, we change the sign/operator to opposite. Ergo, changing from plus to minus and multiply to divide.
[tex]5x = 19 + 7 \\ 5x = 26[/tex]
We are at this part. Now to move 5 which is multiplying the x. So we move 5 from multiply to divide 26.
[tex]x = \frac{26}{5} [/tex]
Ergo, the answer is x = 26/5
What is the square root of 166?
Answer:
12.8840987267
Step-by-step explanation:
Answer:
[tex]\sqrt{166}[/tex] = 12.8
Step-by-step explanation:
How to identify the VA and HA in an equation?
9. Given: f(x) = 2x + 3 and g(x) = 3x + 1
Find: (f • g)(-1)
Answer: -2
Step-by-step explanation:
f(x) = 2x + 3, g(x) = 3x + 1
(f • g)(-1)=
f(-1)*g(-1)=
(2(-1)+3)*(3(-1)+1)=
(-2+3)(-3+1)=
1*(-2)=-2
Use long division to find the quotient (16x3 + 4x2 - 144) / (4x - 8)
Answer:
[tex] - 22 x - 8[/tex
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Answer: 4x^2+9x+18
Step-by-step explanation: yes